I would for sure do the two stays. We have done it both ways and staying onsite at Universal is incredible. Nothing ever beats Disney in my book because I like the parks better, but the hotels at Universal are so much nicer than any of the Disney ones. The front of the line access that you can use over and over is just amazing. It is like having fastpasses all day for so many of the rides (Not all of them though) and you also get early access to Harry Potter.
. We did US/IoA first (we always do) and then Disney. It is much easier to fly in and rent a car at the airport. This year we stayed at Portofino Bay. It is a beautiful resort. We are now at the YC for 6 days. It is easier for us to keep the car for a week and then turn it in at the Dolphin and take the Magic Express back to the airport. We hate dragging our luggage at the end of the trip and appreciate the baggage check that Disney offers. It is easier on us at MCO without worrying about checking our bags.
EXPRESS PASS!